Research

I am currently working under the mentorship of Dr. David P. Herzog. We study the asymptotic stability of nonlinear stochastic dynamics. Our most recent pre-print establishes explicit rates of convergence for Langevin dynamics subject to singular potentials in a weighted norm. More recently, we are focusing on the asymptotic behavior of degenerately stochastically forced Lorenz 96 systems.

My mathematical research and interests lie in:

  • Stochastic Processes

  • Chaos Theory and Nonlinear Dynamics

  • Functional Analysis

  • Partial Differential Equations

  • Quantum Mechanics

  • Mathematical Chemistry

A recent presentation of our Langevin dynamics results.

202103121101-Camrud.mp4

Research with Undergraduates

I was privileged enough to participate in mathematics research as an undergraduate at Concordia College, as well as through an NSF-funded research program at New York University. These experiences were invaluable to my future career as a mathematician, and I try to participate in leading undergraduate research whenever possible. The list of program topics I have led with undergraduates includes:

  • Fractals and iterated function systems

  • Sampling and interpolation theory

  • Markov chains and mixing times

  • Models for turbulent flow

  • Semigroup theory

  • Fractional operator theory